-- -*- M2-comint -*- {* hash: 1764380813 *}
i1 : R = ZZ/32003[a..e];
i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (- 2532a - 9974a b + 14360a*b - 2760b - 5788a c - 14141a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
1720b c - 4004a*c - 14487b*c + 7914c - 1916a d - 4926a*b*d + 11481b d
------------------------------------------------------------------------
2 2 2 2
- 5260a*c*d - 11762b*c*d + 14562c d + 4085a*d - 10296b*d + 2440c*d -
------------------------------------------------------------------------
3 2 2
14061d + 12308a e - 3711a*b*e - 3027b e - 11981a*c*e - 9907b*c*e -
------------------------------------------------------------------------
2 2 2
1174c e - 2904a*d*e - 13632b*d*e - 9316c*d*e + 10896d e - 11371a*e -
------------------------------------------------------------------------
2 2 2 3 3 2 2
4289b*e - 13483c*e - 5013d*e + 5882e , 10885a - 15951a b - 6403a*b
------------------------------------------------------------------------
3 2 2 2 2 3
- 6339b + 1076a c - 6352a*b*c - 5925b c - 10949a*c + 3212b*c - 4837c
------------------------------------------------------------------------
2 2 2
- 3818a d + 11724a*b*d - 6641b d + 11788a*c*d + 9674b*c*d - 11154c d -
------------------------------------------------------------------------
2 2 2 3 2
6375a*d + 7778b*d - 14130c*d + 11946d + 15343a e + 3836a*b*e -
------------------------------------------------------------------------
2 2
2450b e + 13768a*c*e + 4491b*c*e + 3578c e - 12836a*d*e + 14116b*d*e +
------------------------------------------------------------------------
2 2 2 2 2
5019c*d*e + 11039d e - 13428a*e + 180b*e - 1422c*e + 6269d*e -
------------------------------------------------------------------------
3 3 2 2 3 2
10776e , 216a - 13285a b + 2864a*b + 8344b + 15554a c - 5406a*b*c -
------------------------------------------------------------------------
2 2 2 3 2 2
2838b c - 12354a*c - 7504b*c - 6529c - 9021a d + 10220a*b*d - 6631b d
------------------------------------------------------------------------
2 2 2 2
+ 15052a*c*d + 12194b*c*d + 12864c d + 14921a*d - 13201b*d + 1720c*d
------------------------------------------------------------------------
3 2 2
+ 12178d - 15772a e - 8851a*b*e - 6670b e - 9343a*c*e - 8345b*c*e -
------------------------------------------------------------------------
2 2 2
2453c e - 12497a*d*e + 4852b*d*e - 14662c*d*e - 3495d e + 14031a*e +
------------------------------------------------------------------------
2 2 2 3
9771b*e - 13675c*e + 5261d*e + 9984e )
o2 : Ideal of R
i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
i4 : g = gb(I,StopBeforeComputation => true);
i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2+10349b3+11746a2c-5669abc+7982b2c+10461ac2-13602bc2-8384c3+7528a2d-
------------------------------------------------------------------------
2837abd+7580b2d-12155acd-1694bcd-9483c2d+1526ad2-8668bd2+6158cd2-4369d3-
------------------------------------------------------------------------
8153a2e-9284abe-8540b2e-13603ace+4919bce-8023c2e+14366ade+14796bde-
------------------------------------------------------------------------
1208cde-9905d2e-11250ae2-15837be2-15176ce2-8027de2-12547e3
------------------------------------------------------------------------
a2b+15441b3+2869a2c-7483abc-2003b2c+10805ac2+11487bc2+5137c3+11014a2d+
------------------------------------------------------------------------
13804abd-11337b2d+8814acd+6928bcd-6902c2d+8429ad2+5286bd2-8939cd2+3856d3
------------------------------------------------------------------------
+5373a2e+7874abe-6053b2e-12276ace+6509bce+3086c2e-10186ade-14308bde-
------------------------------------------------------------------------
5246cde+663d2e+7058ae2-5141be2-13688ce2-6215de2+92e3
------------------------------------------------------------------------
a3+13770b3+11155a2c+1161abc+757b2c+15377ac2-2299bc2-9697c3+12909a2d+
------------------------------------------------------------------------
3628abd-4258b2d+3124acd+12729bcd+15692c2d-14679ad2-15022bd2-114cd2-
------------------------------------------------------------------------
5621d3+9565a2e+8030abe-8246b2e-5618ace-15775bce+1773c2e-7321ade-12959bde
------------------------------------------------------------------------
+3251cde+12672d2e+11574ae2+5551be2-508ce2+6602de2-12245e3
------------------------------------------------------------------------
b3c+8164a2c2-13773abc2-2020b2c2-14012ac3+4182bc3-5949c4-13671b3d+
------------------------------------------------------------------------
13299a2cd-12934abcd-15143b2cd+8499ac2d-11605bc2d-3387c3d+5802a2d2-
------------------------------------------------------------------------
8654abd2-545b2d2+14892acd2-5591bcd2-10408c2d2+3543ad3-1017bd3+1538cd3-
------------------------------------------------------------------------
2960d4-5376b3e+15590a2ce-7677abce+4335b2ce+15250ac2e-8078bc2e-5907c3e-
------------------------------------------------------------------------
745a2de-2518abde+4169b2de-14833acde-11413bcde+3490c2de+6112ad2e-
------------------------------------------------------------------------
12408bd2e+650cd2e+2077d3e-2412a2e2+12580abe2+14254b2e2+5711ace2-
------------------------------------------------------------------------
11468bce2+2191c2e2+9828ade2+3bde2+9023cde2-8197d2e2+5083ae3+15732be3+
------------------------------------------------------------------------
14841ce3+2883de3+11560e4
------------------------------------------------------------------------
b4-15480a2c2+3308abc2-10419b2c2-8301ac3-611bc3-5950c4-14593b3d+13393a2cd
------------------------------------------------------------------------
+11207abcd-7329b2cd+8281ac2d+5241bc2d+15330c3d+10197a2d2+3982abd2-
------------------------------------------------------------------------
13809b2d2-3182acd2-8234bcd2+11030c2d2-9281ad3-1177bd3-8164cd3+8585d4+
------------------------------------------------------------------------
8841b3e+13127a2ce-14740abce+15491b2ce+15613ac2e+7805bc2e+8260c3e+
------------------------------------------------------------------------
11408a2de+6232abde+3594b2de+2266acde-13997bcde+4612c2de-42ad2e+14148bd2e
------------------------------------------------------------------------
-6910cd2e+8666d3e+5846a2e2+3883abe2+9104b2e2-4934ace2+11868bce2+3468c2e2
------------------------------------------------------------------------
-5529ade2-11362bde2-9294cde2+2313d2e2-11270ae3+3849be3+5324ce3-11722de3-
------------------------------------------------------------------------
2532e4 abc3-990b2c3-7ac4-11826bc4-11070c5-14033a2c2d-6873abc2d+1161b2c2d
------------------------------------------------------------------------
+10853ac3d-14090bc3d-1270c4d+11118b3d2-3297a2cd2-8998abcd2-14846b2cd2-
------------------------------------------------------------------------
7663ac2d2-15700bc2d2-4987c3d2-13505a2d3-1753abd3+9861b2d3-13537acd3-
------------------------------------------------------------------------
14942bcd3-11289c2d3+8634ad4-11983bd4+13226cd4+9094d5+11417a2c2e+
------------------------------------------------------------------------
8673abc2e+15258b2c2e+14437ac3e-5193bc3e+1260c4e+7465b3de+15042a2cde-
------------------------------------------------------------------------
8284abcde+12891b2cde-1612ac2de+10693bc2de+1783c3de-15971a2d2e-9709abd2e+
------------------------------------------------------------------------
11166b2d2e-177acd2e+2009bcd2e-2712c2d2e+15793ad3e-11871bd3e-11049cd3e-
------------------------------------------------------------------------
7325d4e-12014b3e2-2205a2ce2-3265abce2-11918b2ce2+6122ac2e2+13951bc2e2+
------------------------------------------------------------------------
2603c3e2-6948a2de2-13371abde2+12004b2de2+15378acde2+2479bcde2-13351c2de2
------------------------------------------------------------------------
-14171ad2e2+12062bd2e2-14762cd2e2-878d3e2-7915a2e3+10208abe3+12082b2e3-
------------------------------------------------------------------------
15376ace3-10139bce3-13746c2e3-13896ade3+14229bde3-9919cde3-416d2e3+
------------------------------------------------------------------------
7489ae4-6968be4+2967ce4-11867de4-10586e5
------------------------------------------------------------------------
a2c3+13539b2c3+4086ac4-2703bc4+4218c5+6748a2c2d+1452abc2d+10911b2c2d+
------------------------------------------------------------------------
2405ac3d+4579bc3d-13792c4d+2651b3d2-9599a2cd2-4531abcd2-7456b2cd2-
------------------------------------------------------------------------
15773ac2d2-15457bc2d2+14677c3d2-9580a2d3-5068abd3+6762b2d3+15026acd3+
------------------------------------------------------------------------
6398bcd3+15593c2d3+5074ad4+10711bd4-1899cd4+8782d5+12796a2c2e-3954abc2e+
------------------------------------------------------------------------
6679b2c2e+10507ac3e-13817bc3e-2495c4e+3803b3de-2324a2cde+2807abcde-
------------------------------------------------------------------------
3370b2cde-10201ac2de-15920bc2de+8467c3de+9522a2d2e+2538abd2e-3039b2d2e-
------------------------------------------------------------------------
9306acd2e-3961bcd2e-7854c2d2e+13086ad3e+12970bd3e+8747cd3e+5185d4e-
------------------------------------------------------------------------
6539b3e2-2154a2ce2+4865abce2+15858b2ce2+11045ac2e2+1844bc2e2-15059c3e2+
------------------------------------------------------------------------
14665a2de2+1875abde2+965b2de2+9058acde2-6202bcde2-14339c2de2-8954ad2e2-
------------------------------------------------------------------------
115bd2e2+10297cd2e2+5901d3e2+12539a2e3+9268abe3-10933b2e3-15451ace3-
------------------------------------------------------------------------
2023bce3+7283c2e3+11003ade3-2582bde3-3029cde3-13429d2e3+15739ae4+9470be4
------------------------------------------------------------------------
-4924ce4-10812de4+2538e5 |
1 7
o6 : Matrix R <--- R
i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
i8 :
